Global existence from single-component 𝐿_{𝑝} estimates in a semilinear reaction-diffusion system

Quittner, Pavol; Souplet, Philippe

doi:10.1090/S0002-9939-02-06453-5

Global existence from single-component $L_{p}$ estimates in a semilinear reaction-diffusion system

Authors: Pavol Quittner and Philippe Souplet
Journal: Proc. Amer. Math. Soc. 130 (2002), 2719-2724
MSC (1991): Primary 35B60, 35K50, 35K60
DOI: https://doi.org/10.1090/S0002-9939-02-06453-5
Published electronically: February 4, 2002
MathSciNet review: 1843418
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Abstract: For a system of two reaction-diffusion equations coupled by power nonlinearities, we prove that an $L_{p}$ bound on a single component for suitable is enough to guarantee global existence. Also we provide a strong indication that our condition on is the best possible. Moreover, this continuation result is in contrast with the corresponding necessary and sufficient conditions for local existence obtained earlier by the authors.

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